This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A144388 A triangle of coefficients for polynomials: p(x,n)=(x + 1)^n - n*(x - 1)^(n - 1). 0

%I

%S 1,0,1,3,0,1,-2,9,0,1,5,-8,18,0,1,-4,25,-20,30,0,1,7,-24,75,-40,45,0,

%T 1,-6,49,-84,175,-70,63,0,1,9,-48,196,-224,350,-112,84,0,1,-8,81,-216,

%U 588,-504,630,-168,108,0,1,11,-80,405,-720,1470,-1008,1050,-240,135,0,1

%N A triangle of coefficients for polynomials: p(x,n)=(x + 1)^n - n*(x - 1)^(n - 1).

%C Row sums are:

%C {1, 1, 4, 8, 16, 32, 64, 128, 256, 512, 1024}.

%F p(x,n)=(x + 1)^n - n*(x - 1)^(n - 1); t(n,m)=coefficients(p(x,n)).

%e {1},

%e {0, 1},

%e {3, 0, 1},

%e {-2, 9, 0, 1},

%e {5, -8, 18, 0, 1},

%e {-4, 25, -20, 30, 0, 1},

%e {7, -24, 75, -40, 45, 0, 1},

%e {-6, 49, -84, 175, -70, 63, 0, 1},

%e {9, -48, 196, -224, 350, -112, 84, 0, 1},

%e {-8, 81, -216, 588, -504, 630, -168, 108, 0, 1},

%e {11, -80, 405, -720, 1470, -1008, 1050, -240, 135, 0, 1}

%t Clear[p, x, n]; p[x_, n_] = (x + 1)^n - n*(x - 1)^(n - 1); Table[ExpandAll[p[x, n]], {n, 0, 10}]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]

%K uned,sign

%O 1,4

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 01 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .